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Moduli-dependent Calabi-Yau and SU(3)-structure metrics from Machine Learning

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arxiv 2012.04656 v2 pith:UJZGUCMO submitted 2020-12-08 hep-th

Moduli-dependent Calabi-Yau and SU(3)-structure metrics from Machine Learning

Lara B. Anderson , Mathis Gerdes , James Gray , Sven Krippendorf , Nikhil Raghuram , Fabian Ruehle This is my paper
classification hep-th
keywords structuremetricscalabi-yaulearningmachinecrucialmethodsstring
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We use machine learning to approximate Calabi-Yau and SU(3)-structure metrics, including for the first time complex structure moduli dependence. Our new methods furthermore improve existing numerical approximations in terms of accuracy and speed. Knowing these metrics has numerous applications, ranging from computations of crucial aspects of the effective field theory of string compactifications such as the canonical normalizations for Yukawa couplings, and the massive string spectrum which plays a crucial role in swampland conjectures, to mirror symmetry and the SYZ conjecture. In the case of SU(3) structure, our machine learning approach allows us to engineer metrics with certain torsion properties. Our methods are demonstrated for Calabi-Yau and SU(3)-structure manifolds based on a one-parameter family of quintic hypersurfaces in $\mathbb{P}^4.$

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